One of the best big-wave surfers in the world has made a 20,000-mile round trip from Hawaii to ride the massive waves that recent storms have brought to the shores of Europe.

Shane Dorian caught just two of the 20-metre waves off the French coast, but that was enough to justify the trip for his sponsors, seeking exposure for the increasingly high-profile sport of big-wave riding.

Dorian was at home with his family in the Hawaiian district of Kona last week when he received an email from France putting him on standby that "something special was brewing". It was the so-called "black swell", the vast low-pressure system that has lashed the Europe's Atlantic coast this week from Portugal in the south to Ireland in the north, creating monster waves.

Dorian, 41, who is one of a select band of professional big-wave surfers who spend their days poring over global swell charts, had been waiting for this moment and dropped everything to travel 30 hours via Honolulu, Los Angeles and Munich to Bilbao for a chance to ride Belharra, a famous deepwater break a mile out to sea off the French Basque country.

The Hawaiian was one of the world's best competition surfers before he turning to the extreme sport of big-wave riding and last year he won the $50,000 (£30,000) Billabong XXL award for the best wave of 2013 when he paddled into Jaws, a fearsome break off Maui. He has surfed the biggest waves off Mexico, California, Fiji and Tahiti, but Belharra was a peak he had yet to scale.

His imperative was simple: ride the biggest wave he could find and in the process get exposure for his various sponsors, through photographs, videos, online coverage and on the front of surfing magazines. It is a job, he explains, not dissimilar to driving a Formula One racing car covered in corporate logos and looking for a global audience. On Tuesday Belharra became his Monaco grand prix.

He arrived in France on Sunday night and the swell built and built before he and a group of other surfers took a boat out to the break. His plan was to try and use his own body strength to paddle into the wave rather than be towed in by a jet ski as most big-wave surfers prefer. It is a purist approach that adds to the danger of getting it wrong.

The waves on Tuesday towered up to 20 metres and moved at 25mph so without any mechanical assistance and in a howling wind, to be in the right place to avoid an immediate and potentially fatal wipeout required every bit of his 16 years of experience as a professional.

"I was pretty nervous because there was some heat behind the swell," he told the Guardian shortly after coming out of the sea, still suffering jetlag. "I had some serious butterflies in my stomach."

He managed to catch two waves, not many perhaps for a 20,000-mile round trip, but size, not quantity is what counts on the big wave circuit. Even for a veteran, the reality of surfing in winter storm Hercules was "terrifying".

"It is very, very scary," he said of the moment before he launched himself. "Everything in your gut and your instinct is telling you to paddle over the wave and you have to overcome those feelings and dig deep. Overcoming that is very stressful, but it feels very good afterwards.

"It is like staring down the wall of a building. There's a feeling of accomplishment in overcoming what your mind and body wanted to do. At the end of a day it is pretty taxing because you have been on an emotional rollercoaster, but that is the pursuit: overcoming your fears."

Once those fears were overcome, he described how his extra-long 3.5-metre board hammered down the wave face towards safety.

"You are so focused on your own world and using your experience to ride the wave without falling that you don't notice anything," he said. "You are in your little moment and you hang on for dear life."

There's not much time to reflect on his achievement. He will fly straight back to Hawaii, where another big swell is forecast.

"Every single day I am looking at the charts and seeing what is brewing," he said. For Dorian and the other big-wave surfers, it is an endless winter.